Identifiability of causal effects for binary variables with baseline data missing due to death.

Area of Science:

• Causal inference
• Biostatistics
• Epidemiology

Background:

• Estimating causal effects in subgroups is challenging when covariates are missing.
• Death can cause covariate missingness, distinct from outcome censoring.
• Previous methods relied on strong monotonicity (SM) assumptions.

Purpose of the Study:

• To investigate the identifiability and estimation of causal effects in subgroups with death-missing covariates.
• To relax the strong monotonicity (SM) assumption to monotonicity (M) and no-interaction (NI).
• To develop methods for estimating causal effects under weaker assumptions.

Main Methods:

• Focus on identifiability of the joint distribution of covariate, treatment, and potential outcomes.
• Derivation of expectation-maximization (EM) algorithms for maximum likelihood estimation.
• Relaxation of SM to M and NI assumptions, and their subsequent removal.

Main Results:

• Sufficient conditions for identifiability of the joint distribution are established.
• EM algorithms are derived for parameter estimation under various assumptions.
• Signs of causal effects in subgroups are proven to be identifiable, even without M and NI assumptions.

Conclusions:

• The study provides a robust framework for causal effect estimation with death-missing covariates.
• The developed methods relax restrictive assumptions, enhancing applicability.
• Identifiability of causal effect signs offers valuable insights even when full estimation is not possible.